The Adaptive Hierarchical Fair Competition (HFC) Model for EA’s

1. The Adaptive Hierarchical Fair Competition (HFC) Model for EA’s Jianjun Hu, Erik D. Goodman Kisung Seo, Min Pei Genetic Algorithm Research &Applications Group (GARAGe) Department of Computer Science & Engineering Department of Electrical and Computer Engineering Michigan State University Presented at GECCO, 2002, New York

2. Outline of this talk • Motivation of Adaptive HFC model • HFC: Metaphor from Societal and Biological Systems • HFC Algorithm • Limitations of HFC • Adaptive HFC: toward autonomous EA’s • AHFC with adaptive admission thresholds • Experiments • Conclusion and future work

3. Motivation for Adaptive HFC Model • The Holy Grail of EC: Autonomous EC • Algorithm parameters adaptive to problem space • Algorithm structure adaptive to problem space • Efficient and robust • AHFC- an Adaptive Parallel (multi-population) EA model

4. Motivation for HFC Model: Fighting Premature Convergence. • Why & how premature convergence occurs? • Exploiting best individuals loss of diversity reduced ability to explore • Higher average fitness harder to explore • High rates of mutation(crossover, too, in GP) unproductive diversity • New (or random) individuals with quite different genetic makeup usually have low fitness and produce few offspring less chance to explore and exploit new peaks  premature convergence! Our conclusion: unfair competition leads to premature convergence.

5. HFC : Metaphor from Societal Systems • Q: how to protect new but promising individuals with low fitness? • A: fair competition mechanism in sports, chess, education systems • Competition allowed only among candidates with comparable capabilities • Competition organized into hierarchical levels • Child prodigies recognized, advanced • Protects young candidates, reduces unfair competition Our solution: Fair Competition by levels.

6. HFC Model for EAs Main Points: • Ensure fair competition among individuals • Protect young (low-fitness) individuals while exploiting higher-fitness ones • Stratify the individuals into a hierarchy of fitness levels • Export individuals by moving out, not copying • Introduce random individuals continually

7. HFC: Structure of the Algorithm • Multi-population • Multiple fitness levels with admission thresholds export thresholds • Each level may have one or more subpopulations • Admission buffers: allows asynchronous HFC • Migration by moving individuals to the level whose fitness range includes their fitness • Random individuals imported to base level continually

8. Adaptation in HFC Model • Adaptive topologies: assigning subpopulations to levels using: • Sliding subpopulation(s) • Topology metamorphosis • Adaptive number of levels • Adaptive admission thresholds • Difficult to set good thresholds before searching • Too high admission threshold gap may make HFC get stuck. • separation of individuals should depend on relative fitnesses

9. AHFC: HFC with adaptive thresholds

10. AHFC: Pseudocode Determine normal EA parameters and nLevel: Number of levels of the hierarchy nCalibGen: Number of generations for initial calibration of thresholds nUpdateGen: Number of generations between admission threshold updates nExch: Number of generations between admission process exchanges 1. During calibration stage Run EA without migration. 2. At the end of calibration stage Compute the mean fitness of whole population, Compute std dev of the whole population, Find the max fitness of whole population, Distribute the admission thresholds even between and 3. At threshold update stage Compute mean fitness & std dev of highest level, and Find the max fitness of highest level, Distribute the admission thresholds even between and

11. Experiment: Eigenvalue Problem —Dynamic System Synthesis by GP • Eigenvalue problem --- difficult synthesis problem requiring simultaneous search of topology and parameters Synthesize a dynamic system (for example, electrical circuit) such that the eigenvalues of the state equation are at the target values. • Problem instances with different degrees of difficulty: 6- to 12-eigenvalue problems

12. AHFC, HFC Parameter Settings

13. Results for 6-, 8-Eigenvalue Problems

14. Results for 10-, 12-Eigenvalue Problems

15. Observations & Conclusions • Both HFC and AHFC do much better than single population GP and standard multi-population GP with little additional computation effort • For simpler problems, AHFC can outperform the HFC version that uses admission thresholds determined based on our experience with the problem space • For more difficult problems, AHFC can approximate the static HFC performance, but is a little less effective • For difficult problems, more levels are highly preferred • HFC and AHFC are well suited for difficult problems

16. Future Work • Adaptive determination of number of levels • Performance monitoring mechanism to decide migrations • More sophisticated admission threshold adaptation mechanism based on qualification ratio • Multi-processor parallel implementation of HFC and testing on huge problems.

17. Acknowledgements • National Science Foundation, Design, Manufacture, and Industrial Innovation Program, grant number DMI-0084934 • Our NSF GP/Bond Graph research group collaborators: • Prof. Ronald C. Rosenberg • Zhun Fan • More information Google search keywords: MSU, HFC